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2 years ago

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A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than

60,000 miles. The manufacturer tests 250 tires and finds the mean life for these tires to be 64,500 miles.What is the alternative hypothesis being tested in this example

1 answer:

aleksandrvk [35]2 years ago

4 0

Answer:

The alternative hypothesis being tested in this example is that the tire life is of more than 60,000 miles, that is:

$H_1: \mu > 60,000$

Step-by-step explanation:

A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles.

At the null hypothesis, we test if the tire life is of at most 60,000 miles, that is:

$H_0: \mu \leq 60,000$

At the alternative hypothesis, we test if the tire life is of more than 60,000 miles, that is:

$H_1: \mu > 60,000$

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Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters t

SashulF [63]

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

Angle of elevation = 60°

Angle of elevation 50 m back = 30°

As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be $h$ meters and $h= h_1+h_s$ .

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ. In ΔSPR.

⇒ $tan(60) = \frac{h_1}{x}$ ...equation (i) ⇒ $tan (30)=\frac{h_1}{x+50}$ ...equation (ii)

Dividing equation (i) and (ii)

⇒ $\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}$

⇒ $3 = \frac{x+50}{x}$

⇒ $3x=x+50$

⇒ $3x-x=50$

⇒ $2x=50$

⇒ $x=\frac{50}{2}$

⇒ $x=25$ meters

To find $h_1$ plugging $x=25$ in equation (i)

⇒ $h_1=x\times tan(60)$

⇒ $h_1=25\times 1.73$

⇒ $h_1=43.25$ meters

The height of the cliff from ground :

⇒ $h= h_1+h_s$

⇒ $h= 43.25+1.8$

⇒ $h=45.05$ meters

The cliff is 45 m tall to the nearest meter.

8 0

2 years ago

Approximately how much principal would need to be placed into an account earning 3.575% interest compounded quarterly so that it

Ainat [17]

<u>Answer-</u>

<em>$23377</em><em> must be deposited to get $68000 at the end of 30 years.</em>

<u>Solution-</u>

We know that for compound interest,

$A=P(1+\dfrac{r}{n})^{nt}$

Where,

A = Future amount = $68,000

P = ??

r = 3.575% annual = 0.03575

n = 4 as interest is compounded quarterly

t = time in year = 30 years

Putting the values,

$\Rightarrow 68000=P(1+\dfrac{0.03575}{4})^{4\times 30}$

$\Rightarrow 68000=P(1.0089375)^{120}$

$\Rightarrow P=\dfrac{68000}{(1.0089375)^{120}}$

$\Rightarrow P=23377.45$

Therefore, $23377 must be deposited to get $68000 at the end of 30 years.

7 0

2 years ago

Read 2 more answers

On average, indoor cats live to 16 years old with a standard deviation of 2.5 years. Suppose that the distribution is normal. Le

Y_Kistochka [10]

Answer:

(a) N (16, 2.5²)

(b) 0.241

(c) Low: 15.4 years

High: 16.6 years

Step-by-step explanation:

The random variable <em>X</em> is defined as the age at death of a randomly selected indoor cat.

(a)

The distribution of X is:

$X\sim N(\mu = 16, \sigma^{2}=2.5^{2})$

(b)

Compute the probability that an indoor cat dies when it is between 17.2 and 19.6 years old as follows:

$P(17.2$

$=P(0.48$

Thus, the probability that an indoor cat dies when it is between 17.2 and 19.6 years old is 0.241.

(c)

Compute the two numbers within which 20% of indoor cats' age of death lies as follows:

$P(x_{1}$

The corresponding value of <em>z</em> is, 0.25.

Compute the value of <em>x</em>₁ and <em>x</em>₂ as follows:

$z=\frac{x_{1}-\mu}{\sigma}\\\\0.25=\frac{x_{1}-16}{2.5}\\\\x_{1}=16+(0.25\times 2.5}\\\\x_{1}=16.625\\\\x_{1}\approx 16.6$ $z=\frac{x_{1}-\mu}{\sigma}\\\\-0.25=\frac{x_{2}-16}{2.5}\\\\x_{2}=16-(0.25\times 2.5}\\\\x_{2}=15.375\\\\x_{2}\approx 15.4$

Low: <u>15.4</u> years

High: <u>16.6</u> years

8 0

2 years ago

Which is the graph of linear inequality x – 2y ≥ –12?

galben [10]

Answer:

option D

Step-by-step explanation:

x-2y≥-12

-2y≥-x-12

y≤0.5x+6

has to be a solid line since y is less than or equal to 0.5x+6

so, options 1 and 3 are not applicable

also, in y≤0.5x+6 , y is less than or equal to this line, thus it only exists on the line and to the right of it (below it)

so, option 2 is wrong also, leaving us with option 4 or D, which in this case is the answer

I attached a file of this inequality's graph to prove my answer once more

4 0

2 years ago

What is the volume of a cylindrical bucket that is 35 cm tall and has a base with a diameter of 21 cm? Use Pi = StartFraction 22

Naya [18.7K]

Answer:

The volume of the cylindrical bucket to the nearest tenth of a cubic centimeter is 12,122.6 cm^3

Step-by-step explanation:

In this question, we are asked to calculate the volume of a cylindrical bucket with height 35cm and a base diameter of 21cm

Mathematically, the volume of the cylinder V can be calculated using the formula;

V = π * r^2 * h

The value of π = 22/7

since D = 21cm, r = D/2 = 21/2 = 10.5cm

Substituting these values, we have

V = 22/7 * 10.5^2 * 35 = 12,122.621

To the nearest tenth of a cubic centimeter is 12,122.6 cm^3

8 0

2 years ago

Read 2 more answers